`a)`

ĐKXĐ : 

`{(9-x^2 ne 0),(x+3 ne 0):}`

`<=> {(x ne +-3),(x ne -3):}`

`<=> x ne +-3`

`P=[x^2-6x+9]/[9-x^2]+[4x+8]/[x+3]`

`P=[(x-3)^2]/[-(x-3)(x+3)]+[4x+8]/[x+3]`

`P=[x-3]/[-(x+3)]+[4x+8]/[x+3]`

`P=[3-x]/[x+3]+[4x+8]/[x+3]`

`P=[3-x+4x+8]/[x+3]`

`P=[3x+11]/[x+3]`

`b)`

Khi `x=7` ta có

`P=[3*7+11]/[7+3]`

`P=32/10`

`P=16/5`

`c)`

`P` nguyên khi

`[3x+11]/[x+3] in ZZ`

`-> [3x+9+2]/[x+3] in ZZ`

`-> 3+2/[x+3] in ZZ`

`-> 2/[x+3] in ZZ`

`-> x+3 in Ư(2)`

`-> x+3 in {+-1;+-2}`

`-> x in {-2;-4;-1;-5}` (nhận)